Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estima...Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.展开更多
Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of ...Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.展开更多
By making use of Thiele-type bivariate branched continued fractions and Sumelson inverse,we construct a few kinds of bivariate vector valued rational interpolonts (BVRIs) over rectangular grids and find out certain re...By making use of Thiele-type bivariate branched continued fractions and Sumelson inverse,we construct a few kinds of bivariate vector valued rational interpolonts (BVRIs) over rectangular grids and find out certain relations among these BVRIs such as boundary identity and duality.展开更多
It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem o...It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem of convergence and control the occurrence of real poles.In this paper,we establish a family of linear Hermite barycentric rational interpolants r that has no real poles on any interval and in the case k=0,1,2,the function r^(k)(x)converges to f^(k)(x)at the rate of O(h^3d+3-k)as h→0 on any real interpolation interval,regardless of the distribution of the interpolation points.Also,the function r(x)is linear in data.展开更多
Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms ...Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,展开更多
In this note we present a constructive proof of symmetrical determinantal formulas forthe numerator and denominator of an ordinary rational interpolant,consider the confluencecase and give new determinantal formulas o...In this note we present a constructive proof of symmetrical determinantal formulas forthe numerator and denominator of an ordinary rational interpolant,consider the confluencecase and give new determinantal formulas of the rational interpolant by means of Lagrange’sbasis functions.展开更多
The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively f...The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.展开更多
In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a s...In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.展开更多
A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essential...A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.展开更多
Human motion modeling is a core technology in computer animation,game development,and humancomputer interaction.In particular,generating natural and coherent in-between motion using only the initial and terminal frame...Human motion modeling is a core technology in computer animation,game development,and humancomputer interaction.In particular,generating natural and coherent in-between motion using only the initial and terminal frames remains a fundamental yet unresolved challenge.Existing methods typically rely on dense keyframe inputs or complex prior structures,making it difficult to balance motion quality and plausibility under conditions such as sparse constraints,long-term dependencies,and diverse motion styles.To address this,we propose a motion generation framework based on a frequency-domain diffusion model,which aims to better model complex motion distributions and enhance generation stability under sparse conditions.Our method maps motion sequences to the frequency domain via the Discrete Cosine Transform(DCT),enabling more effective modeling of low-frequency motion structures while suppressing high-frequency noise.A denoising network based on self-attention is introduced to capture long-range temporal dependencies and improve global structural awareness.Additionally,a multi-objective loss function is employed to jointly optimize motion smoothness,pose diversity,and anatomical consistency,enhancing the realism and physical plausibility of the generated sequences.Comparative experiments on the Human3.6M and LaFAN1 datasets demonstrate that our method outperforms state-of-the-art approaches across multiple performance metrics,showing stronger capabilities in generating intermediate motion frames.This research offers a new perspective and methodology for human motion generation and holds promise for applications in character animation,game development,and virtual interaction.展开更多
In this paper,the free vibration and stationary stochastic response of functionally graded(FG)rectangular plates with varying thickness in supersonic flow and thermal environment are analyzed.Two types of material pro...In this paper,the free vibration and stationary stochastic response of functionally graded(FG)rectangular plates with varying thickness in supersonic flow and thermal environment are analyzed.Two types of material property variations of FG plates with varying thickness are considered:the variation along the direction perpendicular to the mid-surface and that along the direction perpendicular to the bottom surface.Considering the effects of aerodynamic pressure and thermal load,the governing equations of motion of FG plates with varying thickness are derived using Hamilton’s principle within the framework of first-order shear deformation theory.A meshfree Jacobi radial point interpolation(Jacobi-RPI)shape function is constructed by combining the Jacobi polynomials and radial basis to approximate the displacement components of the plate.The accuracy and reliability of the present approach are confirmed through sufficient comparisons with numerical results from the published literature and the finite element software ABAQUS.Finally,the effects of different parameters on the free vibration and stationary stochastic response of FG plates are investigated.展开更多
Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture ...Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H^(2)-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.展开更多
Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class...Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class of C-1 discrete tetrahedral interpolants with only C-1 data required. As special cases of the class characterized, we give two C-1 discrete tetrahedral interpolants which have concise expressions.展开更多
Algorithms to generate a triangular or a quadrilateral interpolant with G^1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral ...Algorithms to generate a triangular or a quadrilateral interpolant with G^1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving Bezier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implemented based on the algorithm which can be used to generate and manipulate solid objects in an interactive way.展开更多
Focuses on a study that presented an axiomatic definition to bivariate vector valued rational interpolation on distinct plane interpolation points. Definition; Existence and uniqueness; Connection.
Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional mo...Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional motions of each axis in the higher-order topology modification technique and how to accurately add the different movements expressed in the form of higher-order polynomials to the corresponding motion axes of the machine tool,a flexible higher-order gear topology modification technique based on an electronic gearbox is proposed.Firstly,a two-parameter topology gear surface equation and a grinding model of wheel grinding gears are established,and the axial feed and tangential feed are expressed in a fifth-order polynomial formula.Secondly,the polynomial coefficients are solved according to the characteristics of the point contact when grinding gears.Finally,an improved electronic gearbox model is constructed by combining the polynomial interpolation function to achieve gear topology modification.The validity and feasibility of the modification method based on the electronic gearbox are verified by experimental examples,which is of great significance for the machining of modification gears based on the continuous generative grinding method of the worm grinding wheel.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
Substantial advancements have been achieved in Tunnel Boring Machine(TBM)technology and monitoring systems,yet the presence of missing data impedes accurate analysis and interpretation of TBM monitoring results.This s...Substantial advancements have been achieved in Tunnel Boring Machine(TBM)technology and monitoring systems,yet the presence of missing data impedes accurate analysis and interpretation of TBM monitoring results.This study aims to investigate the issue of missing data in extensive TBM datasets.Through a comprehensive literature review,we analyze the mechanism of missing TBM data and compare different imputation methods,including statistical analysis and machine learning algorithms.We also examine the impact of various missing patterns and rates on the efficacy of these methods.Finally,we propose a dynamic interpolation strategy tailored for TBM engineering sites.The research results show that K-Nearest Neighbors(KNN)and Random Forest(RF)algorithms can achieve good interpolation results;As the missing rate increases,the interpolation effect of different methods will decrease;The interpolation effect of block missing is poor,followed by mixed missing,and the interpolation effect of sporadic missing is the best.On-site application results validate the proposed interpolation strategy's capability to achieve robust missing value interpolation effects,applicable in ML scenarios such as parameter optimization,attitude warning,and pressure prediction.These findings contribute to enhancing the efficiency of TBM missing data processing,offering more effective support for large-scale TBM monitoring datasets.展开更多
Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design o...Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.展开更多
The influence of ocean environment on navigation of autonomous underwater vehicle(AUV)cannot be ignored.In the marine environment,ocean currents,internal waves,and obstacles are usually considered in AUV path planning...The influence of ocean environment on navigation of autonomous underwater vehicle(AUV)cannot be ignored.In the marine environment,ocean currents,internal waves,and obstacles are usually considered in AUV path planning.In this paper,an improved particle swarm optimization(PSO)is proposed to solve three problems,traditional PSO algorithm is prone to fall into local optimization,path smoothing is always carried out after all the path planning steps,and the path fitness function is so simple that it cannot adapt to complex marine environment.The adaptive inertia weight and the“active”particle of the fish swarm algorithm are established to improve the global search and local search ability of the algorithm.The cubic spline interpolation method is combined with PSO to smooth the path in real time.The fitness function of the algorithm is optimized.Five evaluation indexes are comprehensively considered to solve the three-demensional(3D)path planning problem of AUV in the ocean currents and internal wave environment.The proposed method improves the safety of the path planning and saves energy.展开更多
文摘Both the Newton interpolating polynomials and the Thiele-type interpolating continued fractions based on inverse differences are used to construct a kind of bivariate blending rational interpolants and an error estimation is given.
基金Supported by the Project Foundation of the Department of Education of Anhui Province(KJ2008A027,KJ2010B182,KJ2011B152,KJ2011B137)Supported by the Grant of Scientific Research Foundation for Talents of Hefei University(11RC05)Supported by the Grant of Scientific Research Foundation Hefei University(11KY06ZR)
文摘Newton＇s polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae.
基金Supported by the National Natural Science Foundation of China.
文摘By making use of Thiele-type bivariate branched continued fractions and Sumelson inverse,we construct a few kinds of bivariate vector valued rational interpolonts (BVRIs) over rectangular grids and find out certain relations among these BVRIs such as boundary identity and duality.
基金Supported by the National Natural Science Foundation of China(Grant No.11601224)the Science Foundation of Ministry of Education of China(Grant No.18YJC790069)+1 种基金the Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.18KJD110007)the National Statistical Science Research Project of China(Grant No.2018LY28)。
文摘It is well-known that Hermite rational interpolation gives a better approximation than Hermite polynomial interpolation,especially for large sequences of interpolation points,but it is difficult to solve the problem of convergence and control the occurrence of real poles.In this paper,we establish a family of linear Hermite barycentric rational interpolants r that has no real poles on any interval and in the case k=0,1,2,the function r^(k)(x)converges to f^(k)(x)at the rate of O(h^3d+3-k)as h→0 on any real interpolation interval,regardless of the distribution of the interpolation points.Also,the function r(x)is linear in data.
基金Supported by-the National Natural Science Foundation of China
文摘Efficient algorithms are established for the computation of bivariate lacunary vector valued rational interpolants based on the branched continued fractions and a numerical example is given to show how the algorithms are implemented,
文摘In this note we present a constructive proof of symmetrical determinantal formulas forthe numerator and denominator of an ordinary rational interpolant,consider the confluencecase and give new determinantal formulas of the rational interpolant by means of Lagrange’sbasis functions.
文摘The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.
基金the National Natural Science Foundation of China （No. 60473114） the Natural Science Foundation of Auhui Province （No. 070416227）+2 种基金 the Natural Science Research Scheme of Education Department of Anhui Province （No. KJ2008B246） Colleges and Universities in Anhui Province Young Teachers Subsidy Scheme （No. 2008jq1110） the Science Research Foundation of Chaohu College （No. XLY-200705）.
文摘In this paper,a necessary and sufficient condition for the existence of a kind of bivariate vector valued rational interpolants over rectangular grids is given.This criterion is an algebraic method,i.e.,by solving a system of equations based on the given data,we can directly test whether the relevant interpolant exists or not.By coming up with our method, the problem of how to deal with scalar equations and vector equations in the same system of equations is solved.After testing existence,an expression of the corresponding bivariate vector-valued rational interpolant can be constructed consequently.In addition,the way to get the expression is different from the one by making use of Thiele-type bivariate branched vector-valued continued fractions and Samelson inverse which are commonly used to construct the bivariate vector-valued rational interpolants.Compared with the Thiele-type method,the one given in this paper is more direct.Finally,some numerical examples are given to illustrate the result.
文摘A new kind of matrix-valued rational interpolants is recursively established by means of generalized Samelson inverse for matrices, with scalar numerator and matrix-valued denominator. In this respect, it is essentially different from that of the previous works [7, 9], where the matrix-valued rational interpolants is in Thiele-type continued fraction form with matrix-valued numerator and scalar denominator. For both univariate and bivariate cases, sufficient conditions for existence, characterisation and uniqueness in some sense are proved respectively, and an error formula for the univariate interpolating function is also given. The results obtained in this paper are illustrated with some numerical examples.
基金supported by the National Natural Science Foundation of China(Grant No.72161034).
文摘Human motion modeling is a core technology in computer animation,game development,and humancomputer interaction.In particular,generating natural and coherent in-between motion using only the initial and terminal frames remains a fundamental yet unresolved challenge.Existing methods typically rely on dense keyframe inputs or complex prior structures,making it difficult to balance motion quality and plausibility under conditions such as sparse constraints,long-term dependencies,and diverse motion styles.To address this,we propose a motion generation framework based on a frequency-domain diffusion model,which aims to better model complex motion distributions and enhance generation stability under sparse conditions.Our method maps motion sequences to the frequency domain via the Discrete Cosine Transform(DCT),enabling more effective modeling of low-frequency motion structures while suppressing high-frequency noise.A denoising network based on self-attention is introduced to capture long-range temporal dependencies and improve global structural awareness.Additionally,a multi-objective loss function is employed to jointly optimize motion smoothness,pose diversity,and anatomical consistency,enhancing the realism and physical plausibility of the generated sequences.Comparative experiments on the Human3.6M and LaFAN1 datasets demonstrate that our method outperforms state-of-the-art approaches across multiple performance metrics,showing stronger capabilities in generating intermediate motion frames.This research offers a new perspective and methodology for human motion generation and holds promise for applications in character animation,game development,and virtual interaction.
文摘In this paper,the free vibration and stationary stochastic response of functionally graded(FG)rectangular plates with varying thickness in supersonic flow and thermal environment are analyzed.Two types of material property variations of FG plates with varying thickness are considered:the variation along the direction perpendicular to the mid-surface and that along the direction perpendicular to the bottom surface.Considering the effects of aerodynamic pressure and thermal load,the governing equations of motion of FG plates with varying thickness are derived using Hamilton’s principle within the framework of first-order shear deformation theory.A meshfree Jacobi radial point interpolation(Jacobi-RPI)shape function is constructed by combining the Jacobi polynomials and radial basis to approximate the displacement components of the plate.The accuracy and reliability of the present approach are confirmed through sufficient comparisons with numerical results from the published literature and the finite element software ABAQUS.Finally,the effects of different parameters on the free vibration and stationary stochastic response of FG plates are investigated.
基金supported by Beijing Natural Science Foundation(L233025)。
文摘Functionally graded material(FGM)plates are widely used in various engineering structures owing to their tailor-made mechanical properties,whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis.These two classes of problems respectively embody material non-uniformity and geometric discontinuity,thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation.Based on the classical Kirchhoff-Love plate theory,a numerical manifold method(MLS-NMM)incorporating moving least squares(MLS)interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects.The method constructs an H^(2)-regular approximation with high-order continuous weighting functions and,combined with the separation of mathematical and physical covers,establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction.For the crack tip,a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment,enabling the natural capture of displacement discontinuity and stress singularity.Stress intensity factors are extracted using the interaction integral method,and the dimensionless J-integral shows a maximum relative error below 1.2%compared with the reference solution.Numerical results indicate that MLS-NMM exhibits excellent convergence performance:using 676 mathematical nodes,the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%,and no shear locking occurs.A systematic analysis reveals that for a simply supported on all four edges(SSSS)FGM square plate with a/h=10,the nondimensional central deflection increases by 212%as the gradient index nrises from 0 to 5.For a homogeneous plate containing a central crack with c/a=0.6,the nondimensional central deflection increases by approximately 46%compared with the intact plate.Under weak boundary constraints(e.g.,SFSF),the deformation is markedly amplified,with the deflection reaching more than three times that under strong constraints(SCSC).The proposed method provides an efficient,reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.
文摘Smooth interpolants defined over tetrahedra are currently being developed for they have many applications in geography, solid modeling, finite element analysis, etc. In this paper, we will characterize a certain class of C-1 discrete tetrahedral interpolants with only C-1 data required. As special cases of the class characterized, we give two C-1 discrete tetrahedral interpolants which have concise expressions.
文摘Algorithms to generate a triangular or a quadrilateral interpolant with G^1-continuity are given in this paper for arbitrary scattered data with associated normal vectors over a prescribed triangular or quadrilateral decomposition. The interpolants are constructed with a general method to generate surfaces from moving Bezier curves under geometric constraints. With the algorithm, we may obtain interpolants in complete symbolic parametric forms, leading to a fast computation of the interpolant. A dynamic interpolation solid modelling software package DISM is implemented based on the algorithm which can be used to generate and manipulate solid objects in an interactive way.
基金the National Natural Science Foundation of China (19871054).
文摘Focuses on a study that presented an axiomatic definition to bivariate vector valued rational interpolation on distinct plane interpolation points. Definition; Existence and uniqueness; Connection.
基金Projects(52275483,52075142,U22B2084)supported by the National Natural Science Foundation of ChinaProject(JZ2023HGPA0292)supported by the Fundamental Research Funds for the Central Universities of China。
文摘Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional motions of each axis in the higher-order topology modification technique and how to accurately add the different movements expressed in the form of higher-order polynomials to the corresponding motion axes of the machine tool,a flexible higher-order gear topology modification technique based on an electronic gearbox is proposed.Firstly,a two-parameter topology gear surface equation and a grinding model of wheel grinding gears are established,and the axial feed and tangential feed are expressed in a fifth-order polynomial formula.Secondly,the polynomial coefficients are solved according to the characteristics of the point contact when grinding gears.Finally,an improved electronic gearbox model is constructed by combining the polynomial interpolation function to achieve gear topology modification.The validity and feasibility of the modification method based on the electronic gearbox are verified by experimental examples,which is of great significance for the machining of modification gears based on the continuous generative grinding method of the worm grinding wheel.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
基金supported by the National Natural Science Foundation of China(Grant No.52409151)the Programme of Shenzhen Key Laboratory of Green,Efficient and Intelligent Construction of Underground Metro Station(Programme No.ZDSYS20200923105200001)the Science and Technology Major Project of Xizang Autonomous Region of China(XZ202201ZD0003G).
文摘Substantial advancements have been achieved in Tunnel Boring Machine(TBM)technology and monitoring systems,yet the presence of missing data impedes accurate analysis and interpretation of TBM monitoring results.This study aims to investigate the issue of missing data in extensive TBM datasets.Through a comprehensive literature review,we analyze the mechanism of missing TBM data and compare different imputation methods,including statistical analysis and machine learning algorithms.We also examine the impact of various missing patterns and rates on the efficacy of these methods.Finally,we propose a dynamic interpolation strategy tailored for TBM engineering sites.The research results show that K-Nearest Neighbors(KNN)and Random Forest(RF)algorithms can achieve good interpolation results;As the missing rate increases,the interpolation effect of different methods will decrease;The interpolation effect of block missing is poor,followed by mixed missing,and the interpolation effect of sporadic missing is the best.On-site application results validate the proposed interpolation strategy's capability to achieve robust missing value interpolation effects,applicable in ML scenarios such as parameter optimization,attitude warning,and pressure prediction.These findings contribute to enhancing the efficiency of TBM missing data processing,offering more effective support for large-scale TBM monitoring datasets.
基金supports for this research were provided by the National Natural Science Foundation of China(No.12272301,12002278,U1906233)the Guangdong Basic and Applied Basic Research Foundation,China(Nos.2023A1515011970,2024A1515010256)+1 种基金the Dalian City Supports Innovation and Entrepreneurship Projects for High-Level Talents,China(2021RD16)the Key R&D Project of CSCEC,China(No.CSCEC-2020-Z-4).
文摘Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper.
基金supported by the High-tech Ship Projects of the Ministry of Industry and Information Technology of China(2021-342).
文摘The influence of ocean environment on navigation of autonomous underwater vehicle(AUV)cannot be ignored.In the marine environment,ocean currents,internal waves,and obstacles are usually considered in AUV path planning.In this paper,an improved particle swarm optimization(PSO)is proposed to solve three problems,traditional PSO algorithm is prone to fall into local optimization,path smoothing is always carried out after all the path planning steps,and the path fitness function is so simple that it cannot adapt to complex marine environment.The adaptive inertia weight and the“active”particle of the fish swarm algorithm are established to improve the global search and local search ability of the algorithm.The cubic spline interpolation method is combined with PSO to smooth the path in real time.The fitness function of the algorithm is optimized.Five evaluation indexes are comprehensively considered to solve the three-demensional(3D)path planning problem of AUV in the ocean currents and internal wave environment.The proposed method improves the safety of the path planning and saves energy.
